The term selectivity ($S$) is used to describe the relative rates of two or more competing reactions on a catalyst. Such competition includes cases of different reactants undergoing simultaneous reactions or of a single reactant taking part in two or more reactions. For the latter case, $S$ may be defined in two ways. The first of these defines a fractional selectivity, $S_{\text{F}}$, for each product by the equation $$S_{\text{F}}=\frac{{\xi }_i}{\sum {\xi }_i}$$ The second defines relative selectivities, $S_{\text{R}}$, for each pair of products by $$S_{\text{R}}=\frac{{\xi }_i}{{\xi }_j}$$ In each case, ${\xi }_i$ and ${\xi }_j$ are the rates of increase of the extent of reactions i and j respectively, i.e. $${\xi }_i=\frac{\mathrm{d}{\xi }_i}{\mathrm{d}t}$$ and $${\xi }_j=\frac{\mathrm{d}{\xi }_j}{\mathrm{d}t}$$ where ${\xi }_i$ and ${\xi }_j$ are the extents of reactions $i$ and $j$ respectively.